1. to manage to get something off (In the sense of getting off a layer from somewhere. "abkriegen" is usually the better choice.)
2. to manage to get/take down (In the sense of getting an object down from somewhere. Can also work for lowering quantities, but it's tricky to use idiomatically.)
Opposite (closest): hochkriegen
3. to manage to put under ("(d)runterkriegen" - has a notion of squeezing stuff under something.)